I am currently training different neural networks for the binary classification of images. When using the logistic regression, my validation loss never increases, even not after 5000 epochs. I thought that at some point overfitting happens and the validation loss always increases. Does anybody know why this does not happen?

Does taking the log of odds bring linearity between the odds of the dependent variable & the independent variables by removing skewness in the data? Is this one reason why we use log of odds in logistic regression? If yes, then is log transformation of data values unnecessary in logistic regression?

When we use logistic regression, we use cross entropy as the loss function. However, based on my understanding and https://machinelearningmastery.com/cross-entropy-for-machine-learning/, cross entropy evaluates if two or more distributions are similar to each other. And the distributions are assumed to be Bernoulli or Multinoulli. So, my question is: why we can always use cross entropy, i.e., Bernoulli in regression problems? Does the real values and the predicted values always follow such distribution?